#40. Two dice are rolled. Let X and Y denote, respectively, the largest and smallest values obtained. Compute the conditional mass function of Y given X = i, i = 1, 2, 3, 4, 5, 6. Are X and Y independent? Why?
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- If X = 1, then P(Y|Y< = X=1) = P(Y=1) = 1/6
- If X = 2, then Pr(Y|Y< = X=2) = P(Y=1 or Y=2) ...
This shows how to compute the conditional mass function for a given dice situation.